A union is things coming together, or uniting, to make one. When the thirteen colonies that became the United States came together, they formed a union. Marriage is another kind of union.
Workers come together to form trade unions so that together they can have a stronger voice negotiating with their employer. The word famously occurs in the Preamble (the introduction) to the United States Constitution: "We the people of the United States, in Order to form a more perfect Union...do ordain and establish this Constitution...." You may recognize the Latin root unum in union, as in e pluribus unum "from many, one," the motto on the seal of the United States.